Toward an adjustable nonlinear low frequency acoustic absorber

A study of the targeted energy transfer (TET) phenomenon between an acoustic resonator and a thin viscoelastic membrane has recently been presented in the paper [R. Bellet et al., Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber, Journal of Sound and Vibration 329 (2010) 2768-2791], providing a new path to passive sound control in the low frequency domain where no efficient dissipative device exists. This paper presents experimental results showing that a loudspeaker used as a suspended piston working outside its range of linearity can also be used as a nonlinear acoustic absorber. The main advantage of this technology of absorber is the perspective to adjust independently the device parameters (mass, nonlinear stiffness and damping) according to the operational conditions. To achieve this purpose, quasi-static and dynamic tests have been performed on three types of commercial devices (one with structural modi?cations), in order to de?ne the constructive characteristics that it should present. An experimental setup has been developed using a one-dimensional acoustic linear system coupled through a box (acting as a weak spring) to a loudspeaker used as a suspended piston acting as an essentially nonlinear oscillator. The tests carried out on the whole vibro-acoustic system have showed the occurrence of the acoustic TET from the acoustic media to the suspended piston and demonstrated the efficiency of this new kind of absorber at low frequencies over a wide frequency range. Moreover, the experimental analyses conducted with different NES masses have con?rmed that it is possible to optimize the noise absorption with respect to the excitation level of the acoustic resonator.     

Essentially nonlinear piezoelectric shunt circuits applied to mistuned bladed disks

An essentially nonlinear piezoelectric shunt circuit is proposed for the practical realization of nonlinear energy sink, and then applied to a mistuned bladed disk for blade vibration reduction. First, the global dynamics of a single degree-of-freedom linear mechanical oscillator, coupled to an essentially nonlinear shunted piezoelectric attachment, is studied. Under certain conditions, the nonlinear targeted energy transfer, i.e. a fast, passive energy transfer from the mechanical oscillator to the nonlinear attachment is observed. A numerical method, referred to as the variable-coefficient harmonic balance method, is developed to calculate quasi-periodic responses arising in the electromechanical system under harmonic forcing. Characterized by the nonexistence of a resonance frequency, the essentially nonlinear shunt circuit is able to work robustly over a broad frequency band with a smaller inductance requirement compared with the linear resonant shunt circuit.     

Frequency intermittency and energy pumping by linear attachments

The present paper considers the problem of realizing an effective targeted energy pumping from a linear oscillator to a set of ungrounded linear resonators attached to it. Theoretical as well as numerical results demonstrate the efficacy of using a complex attachment as a passive absorber of broadband energy injected into the primary structure. The paper unveils also the existence of an instantaneous frequency associated with the master response characterized by intermittency: a rather surprising result for a linear autonomous system. Comparison with nonlinear energy sinks demonstrates that the two systems have some analogies in this respect and that the linear complex attachment is a very efficient energy trap.     

The use of a hybrid model to compute the nonlinear acoustic performance of silencers for the finite amplitude acoustic wave

In the present study, a hybrid method is proposed for predicting the acoustic performance of a silencer for a nonlinear wave. This method is developed by combining two models: (i) a frequency-domain model for the computation of sound attenuation due to a silencer in a linear regime and (ii) a wavenumber space model for the prediction of the nonlinear time-evolution of finite amplitudes of the acoustic wave in a uniform duct of the same length as the silencer. The present method is proposed under the observation that the physical process of the nonlinear sound attenuation phenomenon of a silencer may be decoupled into two distinct mechanisms: (a) a linear acoustic energy loss that owes to the mismatch in the acoustic impedance between reactive elements and/or the sound absorption of acoustic liners in a silencer; (b) a nonlinear acoustic energy loss that is due to the energy-cascade phenomenon that arises from the nonlinear interaction between components of different frequencies. To establish the validity of the present model for predicting the acoustic performance of silencers, two model problems are considered. First, the performance of simple expansion mufflers with nonlinear incident waves has been predicted. Second, proposed method is applied for computing nonlinear acoustic wave propagation in the NASA Langley impedance duct configuration with ceramic tubular liner (CT57). Both results obtained from the hybrid models are compared with those from computational aero-acoustic techniques in a time-space domain that utilize a high-order finite-difference method. Through these comparisons, it is shown that there are good agreements between the two predictions. The main advantage of the present method is that it can effectively compute the nonlinear acoustic performance of silencers in nonlinear regimes without time-space domain calculations that generally entail a greater computational burden.     

Multi-scale energy exchanges between a nonlinear oscillator of Bouc-Wen type and another coupled nonlinear system

The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.     

Enhancing the dynamic range of targeted energy transfer in acoustics using several nonlinear membrane absorbers

In order to enhance the robustness and the energy range of efficiency of targeted energy transfer (TET) phenomena in acoustics, we discuss in this paper about the use of multiple nonlinear membrane absorbers (called nonlinear energy sinks or NES) placed in parallel. We show this way, mainly thanks to an experimental set-up with two membranes, that the different absorbers have additional effects that extend the efficiency and the possibilities of observation of TET. More precisely, we present the different behavior of the system under sinusoidal forcing and free oscillations, characterizing the phenomena for all input energies. The frequency responses are also presented, showing successive clipping of the original resonance peak of the system, and strongly modulated regimes (SMR). A model is finally used to generalize these results to more than two NES and to simulate the case of several very similar membranes in parallel which shows how to extend the existence zone of TET.     

Experimental source characterization techniques for studying the acoustic properties of perforates under high level acoustic excitation

This paper discusses experimental techniques for obtaining the acoustic properties of in-duct samples with non-linear acoustic characteristic. The methods developed are intended both for studies of non-linear energy transfer to higher harmonics for samples only accessible from one side such as wall treatment in aircraft engine ducts or automotive exhaust systems and for samples accessible from both sides such as perforates or other top sheets. When harmonic sound waves are incident on the sample nonlinear energy transfer results in sound generation at higher harmonics at the sample (perforate) surface. The idea is that these sources can be characterized using linear system identification techniques similar to one-port or two-port techniques which are traditionally used for obtaining source data for in-duct sources such as IC-engines or fans. The starting point will be so called polyharmonic distortion modeling which is used for characterization of nonlinear properties of microwave systems. It will be shown how acoustic source data models can be expressed using this theory. Source models of different complexity are developed and experimentally tested. The results of the experimental tests show that these techniques can give results which are useful for understanding non-linear energy transfer to higher harmonics.     

高频聚焦超声声场和温度场的仿真研究

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

主变压器噪声特性分析及复合隔声结构设计*

超高压变电站的主变压器的噪声影响已引起广泛关注。以某典型化设计的500kV变电站A的主变压器为例,进行了现场测试,得到其主变压器噪声能量主要集中在中低频范围内,且具备明显的线谱噪声特征。针对该噪声特点,提出了一种内插微穿孔板的双层带孔板型声学超材料的复合隔声结构。使用传递矩阵理论对该复合结构进行了分析,并在阻抗管中进行了实验验证。实验结果表明：该复合隔声结构具备针对性隔声要求,理论与实验传递损失曲线基本吻合。     

Acoustic wave dispersion in a cylindrical elastic tube filled with a viscous liquid

This paper deals with the study of the velocity and the attenuation of an acoustic wave propagating inside a cylindrical elastic tube filled with a viscous liquid. A theory describing the propagation of the axisymmetrical modes in such waveguides is presented, with special attention given to the absorption produced by the viscous mechanisms in the liquid. One of these mechanisms is related to the momentum transfer between the compression and rarefaction regions of a propagating wave. The other viscous mechanism is due to the momentum transport inside the viscous boundary layer, close to the tube wall. Numerical calculations were carried out to investigate the influence of different parameters (frequency, tube radii, viscosity coefficient) on the propagation of acoustic waves.     

Traveling wave tube measurements for low-frequency properties of underwater acoustic materials

A traveling wave tube measurement technique for measuring acoustic properties of underwater acoustic materials was developed.Water temperature and pressure environments of the ocean can be simulated in a water-filled tube,and the acoustic parameters of samples of underwater acoustic materials are measured in the range of low-frequency.A tested sample is located at central position of the tube.A pair of projectors is separately located at both ends of the tube.Using an active anechoic technique,the sound wave transmitting the tested sample is hardly reflected by the surface of secondary transducer.So the traveling sound field is built up in the tube.By separately calculating the transfer functions of every pair of double hydrophones in the sound fields from the both sides of the sample,its reflection coefficients and transmission coefficients are obtained.In the measurement system,the inside diameter of the tube isΦ208 mm,the working frequency range is from 100 to 4000 Hz,the maximum pressure is 5 MPa.The reflection coefficients and transmission coefficients of a water layer and a stainless steel layer samples are measured actually and calculated theoretically.The results show that the measured values are in good agreement with the values calculated,and the measurement uncertainty is not greater than 1.5 dB.     

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.     

Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning

Dynamical system under investigation in the current work is comprised of harmonically forced linear oscillator with attached nonlinear energy sink. External forcing frequency detuning near the main resonance (1:1) is included in the system investigation. The detailed study of the periodic and quasiperiodic regimes is done in the work via (adaptive) averaging method. Local bifurcations of the periodic regimes are revealed and fully described in the space of system parameters (amplitude of excitation, damping, and frequency detuning). Novel analytical approach for predictions of strongly modulated response (SMR) is presented. This approach provides a sufficient condition for the SMR existence contrary to the previous studies. Various possibilities of coexistence of the response regimes are predicted analytically and demonstrated numerically. Among those is a coexistence of two distinct periodic regimes together with the SMR. All findings of the simplified analytic model are verified numerically and considerable agreement is observed.     

高声压级时多孔金属板的吸声特性研究

针对高声压级下有限厚度多孔金属板在线性阻抗背衬条件下(背衬表面声压与声质点速度为线性关系)的吸声问题,提出了一个描述不同声压级下材料层法向吸声性能的一维模型,并给出求解材料层内部声质点速度的线化与差分方法,以预测多孔金属板在高声压级下的非线性吸声特性。在阻抗管中对两块多孔金属板进行了声学测试,得到了材料层法向表面阻抗和吸声系数随入射声压级变化的实验结果。研究表明:实验与理论预测符合良好,验证了模型与数值方法的正确性。本文所提原理和方法,可用于一般硬质多孔材料。      

Transmission of low-frequency sound through the water-to-air interface

L.M. Brekhovskikh revealed and studied the important role played by inhomogeneous waves emitted by a point source when they pass through an interface with a medium in which the velocity of sound is lower, for example, from water to air. This paper studies the energy characteristics of sound emitted into air by an underwater point source. The energy transfer due to inhomogeneous waves is shown to cause the phenomenon of anomalous transparency of the interface for low-frequency sound. The anomalous transparency manifests itself in that the energy flux through the interface increases with decreasing frequency of sound and, at sufficiently low frequencies, almost all of the acoustic energy produced by the underwater source is emitted into air. Conversely, at high frequencies, when the contribution of the inhomogeneous waves becomes negligible, the water-to-air interface is similar to a perfectly reflecting surface and almost all of the acoustic energy produced by the source is emitted into water. The anomalous transparency phenomenon changes the conventional opinion on the possibility of acoustic coupling between points in water and air and on the role played by physical processes evolving in the water column in generating atmospheric acoustic noise.     

Low temperature acoustic properties of amorphous silica and the tunneling model

Internal friction and speed of sound were measured on a-SiO2 above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, vibrational heating, background losses, and nonlinear effects. Strain amplitudes epsilon(A) = 10(-8) mark the transition between the linear and nonlinear regimes. In the former, agreement with the tunneling model was observed for both internal friction and speed of sound above 25 mK. The observed deviations in the speed of sound below 25 mK can be described with a cutoff energy of Delta(0, min)/k(B) = 6+/-0.5 mK. In the nonlinear regime, above 10 mK the behavior was typical for nonlinear harmonic oscillators, while below 10 mK different behavior was found.     

基于低频吸声超构材料的复合消声器研究*

针对管道内低频噪声难以抑制的问题，本文基于亥姆霍兹共振腔（HR）阵列吸声板和穿孔管消声器组合，设计了一种复合式宽带消声器。首先利用有限元法仿真分析传统穿孔管消声器，发现中低频消声能力较差，通过嵌入HR阵列吸声板吸收中低频噪声。采用仿真与实验的方式研究吸声板的声学性能：在400-1000 Hz频段内的平均吸声系数达到了0.88。然后对复合式消声器进行数值模拟及3D打印阻抗管实验测试对比：复合式消声器在400-1718Hz频率范围内的平均传递损失为18.15 dB ，最终实现了管道内全频带噪声有效控制。     

Nano watermill driven by revolving charge

A novel nanoscale watermill for the unidirectional transport of water molecules through a curved single-walled carbon nanotube(SWNT) is proposed and explored by molecular dynamics simulations. In this nanoscale system, a revolving charge is introduced to drive a water chain confined inside the SWNT, the charge and the tube together serving as a nano waterwheel and nano engine. A resonance-like phenomenon is found, and the revolving frequency of the charge plays a key role in pumping the water chain. The water flux across the SWNT increases with respect to the revolving frequency of the external charge and it reaches its maximum when the frequency is 4 THz. Correspondingly, the number of hydrogen bonds in the water chain inside the SWNT decreases dramatically as the frequency increases from 4 THz to 25 THz. The mechanism behind the resonance phenomenon has been investigated systematically. Our findings are helpful for the design of nanoscale fluidic devices and energy converters.     

Energy pumping for a larger span of energy

This paper is devoted to energy pumping: exhibiting a multi-degree-of-freedom (dof) nonlinear attachment coupled to a single-dof linear one, energy's area leading to energy pumping phenomenon is increased by involving different nonlinear modes in the process.     

Analytical and numerical prediction of harmonic sound power in the inlet of aero-engines with emphasis on transonic rotation speeds

Tone noise radiated through the inlet of a turbofan is mainly due to rotor-stator interactions at subsonic regimes (approach flight), and to the shock waves attached to each blade at supersonic helical tip speeds (takeoff). The axial compressor of a helicopter turboshaft engine is transonic as well and can be studied like turbofans at takeoff. The objective of the paper is to predict the sound power at the inlet radiating into the free field, with a focus on transonic conditions because sound levels are much higher. Direct numerical computation of tone acoustic power is based on a RANS (Reynolds averaged Navier–Stokes) solver followed by an integration of acoustic intensity over specified inlet cross-sections, derived from Cantrell and Hart equations (valid in irrotational flows). In transonic regimes, sound power decreases along the intake because of nonlinear propagation, which must be discriminated from numerical dissipation. This is one of the reasons why an analytical approach is also suggested. It is based on three steps: (i) appraisal of the initial pressure jump of the shock waves; (ii) 2D nonlinear propagation model of Morfey and Fisher; (iii) calculation of the sound power of the 3D ducted acoustic field. In this model, all the blades are assumed to be identical such that only the blade passing frequency and its harmonics are predicted (like in the present numerical simulations). However, transfer from blade passing frequency to multiple pure tones can be evaluated in a fourth step through a statistical analysis of irregularities between blades. Interest of the analytical method is to provide a good estimate of nonlinear acoustic propagation in the upstream duct while being easy and fast to compute. The various methods are applied to two turbofan models, respectively in approach (subsonic) and takeoff (transonic) conditions, and to a Turbomeca turboshaft engine (transonic case). The analytical method in transonic appears to be quite reliable by comparison with the numerical solution and with available experimental data.